As we can see, the probabilities of neutrino flavour, spin and spin-flavour oscillations in general case exhibit quite a complicated interplay of oscillations on different frequencies, that depend on both magnetic \(\mu _i B_{\perp }\)  and vacuum frequencies \(\frac{\Delta m_{ik}^2}{4p}\) . The same phenomenon in the two-flavour case was considered in [1]}, [2]}. Throughout the derivation of the final expression REF , we did not make any assumptions concerning the particular form of the mixing matrix \(U\) , except it being unitary. Thus, the general expression REF  can be used to calculate explicit expressions for the probabilities of neutrino flavour, spin and spin-flavour oscillation in a magnetic field in the three-flavour case. It is easy to show that the two-flavour analytical expressions obtained in [1]} can be retrieved from REF  by setting the mixing angles \(\theta _{13} = \theta _{23} = 0\) , i.e. decoupling \(\nu _{\tau }\)  from \(\nu _e\)  and \(\nu _{\mu }\) . Here we use the standard parametrization of the mixing matrix
\(U=\begin{pmatrix}1 & 0 & 0 \\0 & c_{23} & s_{23} \\0 & -s_{23} & c_{23}\end{pmatrix}\begin{pmatrix}c_{13} & 0 & s_{13} e^{-i\delta } \\0 & 1 & 0 \\-s_{13} e^{i\delta } & 0 & c_{13}\end{pmatrix}\begin{pmatrix}c_{12} & s_{12} & 0 \\-s_{12} & c_{12} & 0 \\0 & 0 & 1\end{pmatrix},\) 
